

from __future__ import annotations

import typing
from collections.abc import Iterable

import numpy as np

lowercase			:				Union[str, Any]   =     typing.Union[Iterable[float], Iterable[int], np.ndarray]  # noqa: UP007
lowercase			:				Union[str, Any]   =     typing.Union[np.floataa, int, float]  # noqa: UP007






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_		):
							return np.sqrt(np.sum((np.asarray(lowerCamelCase_		) - np.asarray(lowerCamelCase_		)) ** 2		)		)






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_		):
							return sum((va - va) ** 2 for va, va in zip(lowerCamelCase_     ,				lowerCamelCase_		)		) ** (1 / 2)


if __name__ == "__main__":






		def        snake_case__		(    ):
									from timeit import timeit

									print('''Without Numpy'''		)
									print(
									    timeit(
									        '''euclidean_distance_no_np([1, 2, 3], [4, 5, 6])'''     ,				number=10000     ,				globals=globals()     ,				)		)
									print('''With Numpy'''		)
									print(
									    timeit(
									        '''euclidean_distance([1, 2, 3], [4, 5, 6])'''     ,				number=10000     ,				globals=globals()     ,				)		)

		benchmark()









from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_     ,				lowerCamelCase_ = "x"     ,				lowerCamelCase_ = 10**-10     ,				lowerCamelCase_ = 1     ,				):
							A      :					int      		=					symbols(lowerCamelCase_		)
							A      :					List[str]      		=					lambdify(lowerCamelCase_     ,				lowerCamelCase_		)
							A      :					Tuple      		=					lambdify(lowerCamelCase_     ,				diff(lowerCamelCase_     ,				lowerCamelCase_		)		)

							A      :					Optional[int]      		=					starting_point

							while True:
														if diff_function(lowerCamelCase_		) != 0:
																					A      :					Union[str, Any]      		=					prev_guess - multiplicity * func(lowerCamelCase_		) / diff_function(
																					    lowerCamelCase_		)
														else:
																					raise ZeroDivisionError('''Could not find root'''		) from None

														# Precision is checked by comparing the difference of consecutive guesses
														if abs(next_guess - prev_guess		) < precision:
																					return next_guess

														A      :					Tuple      		=					next_guess


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(F"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")

		# Find root of polynomial
		# Find fourth Root of 5
		print(F"The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}")

		# Find value of e
		print(
		    "The root of log(y) - 1 = 0 is ",
		    F"{newton_raphson('log(y) - 1', 2, variable='y')}",
		)

		# Exponential Roots
		print(
		    "The root of exp(x) - 1 = 0 is",
		    F"{newton_raphson('exp(x) - 1', 10, precision=0.0_05)}",
		)

		# Find root of cos(x)
		print(F"The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}")






